The effects of connected porosity and graded Lanthanum Strontium Manganate (LSM) particle-based electrodes are analyzed for an electrolyte-supported, Yttria Stabilized Zirconia (YSZ), SOFC half-cell. Optimal microstructure electrodes are proposed by identifying mechanisms that control the transport of oxygen in the porous cathode electrode: 1) transport of oxygen to the cathode-electrolyte interface through the pores; and 2) oxygen replenishment through ion diffusion across the strontium-doped lanthanum manganate (LSM) particulate phase. For the selected material parameters, simulations show that a decrease in the spacing of interconnected porosity improves the power delivery. Microstructural and electrochemical conditions that lead to self-induced starvation of the cell occurs are identified, including the effect of the networks that contribute to power generation in the absence of percolating porosity. Microstructures where LSM particle density gradients are induced demonstrate that a greater number of cathodic particles near the cathode-electrolyte interface increases the power delivery of the cell by improving pore connectivity and thus reducing polarization losses.